Forward sum rule for the 2γ-exchange correction to the charge-radius extraction from elastic electron scattering

Two-photon-exchange (TPE) contributions to elastic electron-proton scattering in the forward regime in leading logarithmic similar to t ln vertical bar t vertical bar approximation in the momentum transfer t are considered. The imaginary part of the TPE amplitude in the forward kinematics is related to the total photoabsorption cross section. The real part of the TPE amplitude is obtained from an unsubtracted fixed-t dispersion relation. This allows a clean prediction of the real part of the TPE amplitude at forward angles with the leading term similar to t vertical bar t vertical bar. Numerical estimates are comparable with or exceed the experimental precision in extracting the charge radius from the experimental data.